{
  "abstract": "In this paper, we study the scaling limit of the pinning model in correlated Gaussian environment. The tail probability of the underlying renewal process of the model has a polynomial decay with exponent $α>0$. The covariance of the Gaussian environment $\\{ω_n\\}_{n\\in\\mathbb N}$ is given by $\\text{Cov}_{\\mathbb P}(ω_n,ω_m)\\sim |n-m|^{2H-2}$ with $H\\in(0,1)$. Assuming $α\\in(0,\\frac12]$, $H\\in(\\frac12,1)$ and $α+2H>2$, we show that the partition function of the disordered pinning model, under the appropriate scaling, converges in distribution to the $L^1$-solution of the fractional stochastic heat equation driven by Gaussian noise correlated in time and localized at the origin. In particular, it is known that the solution is not $L^2$-integrable when $α<\\frac12$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03607",
  "author_total": 3,
  "authors": [
    {
      "name": "Jian Song"
    },
    {
      "name": "Meng Wang"
    },
    {
      "name": "Ran Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7j4yqngbw1bg4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03607",
  "fulltext_url": null,
  "id": "7j4yqngbw1bg4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03607",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7208793049",
  "pdf_url": "https://arxiv.org/pdf/2609.03607",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7j4yqngbw1bg4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03607",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03607"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Scaling limit for the pinning model in correlated Gaussian environment beyond the $L^2$-regime",
  "title_text": "Scaling limit for the pinning model in correlated Gaussian environment beyond the L^2-regime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/7j4yqngbw1bg4",
  "venue": "arXiv",
  "versions": []
}